Ugh. A/C problems have caused me stress. If you get this repaired yourself with a $20 capacitor (maybe less), you win big. At least in my area you won't get one of the local crooks out to replace a capacitor ($20 and 30 minutes total in and out) for less than $400.
I've replaced a couple capacitors, a condenser motor and blower motor over the years. Grainger, Amazon and appliance parts houses usually have whatever you need. My 42 year old unit is still cooling and heating, knock on wood! I dread when something breaks that's not worth fixing because the next unit will cost more, be of less quality and be installed by some kid hyped up on Red Bull.
A couple months ago mine stopped cooling. Found the compressor not kicking on. One of the jumper wires on the... uhh.. thing the main power comes through with the brass contacts and makes a buzzing noise? ... had burned itself into. I replaced it and was back up running.